The generator matrix

 1  0  0  1  1  1 3X+2 3X  1  1 X+2  1  0  1  1  0  1  1  2  1 2X X+2  1  1  2 X+2  1  1 3X+2  X  1  1  1  X 3X  1 3X  1  1  1 2X  1  1  1  2 3X 2X 2X+2  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  2  1  1  1 2X 2X+2  X  1  1 2X+2  0  1  2  1
 0  1  0  0  3 X+1  1  2 3X X+1  1  X  1 X+3 3X+3  1 2X  3  1 2X+2 3X  1  1 2X+3  X  1 3X X+2  1  1 2X+1 X+2  1  2 3X+2 2X+2  1 2X+3 2X+2 3X+3  1 3X+1 2X 2X  1 X+2  2  0 2X 3X+3  1 3X X+2 X+3  0  1 3X+1 3X+2  1  1 X+3  0 X+1 3X+1 X+3  1  X  0  3  X  1  1 2X+2  X  0
 0  0  1  1  1  0  3  1 3X 2X+1 2X X+3 3X+1 2X 3X+1  2 3X  0 2X+1 3X+1  1 3X+1  0 X+1  1  2  3  X  3  X 3X 3X+3 3X+3  1  1 X+2 3X+3 2X+1 3X 3X+2 2X+1 3X+2 X+3 2X+2 2X+1  1  1  1 3X+3  0  3 2X  3 2X+1 X+2  1 X+3 2X+2 X+2  X 3X  1  2 3X+1  X 2X  1 2X  2  3  2 3X+2 3X+1  1  0
 0  0  0  X 3X 2X 3X  X  2 3X  0  0  2 3X+2 2X X+2 X+2 2X+2 X+2 2X+2 3X+2 2X+2 X+2 X+2 2X X+2 3X+2 X+2 3X+2 X+2  X  X  2  0 3X  X  X 2X+2  0 3X+2  0 2X 3X X+2 3X 2X+2 3X 3X+2 3X+2 3X 2X+2  X  0  0 2X+2 3X+2  X 2X  2  0 3X 3X 3X+2 X+2 2X  2  0 X+2 3X 3X 3X+2  2 3X 3X+2  0

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+143x^68+578x^69+1569x^70+2208x^71+2947x^72+3264x^73+4167x^74+3654x^75+4210x^76+3014x^77+2671x^78+1826x^79+1296x^80+620x^81+274x^82+122x^83+81x^84+52x^85+34x^86+14x^87+10x^88+8x^89+5x^90

The gray image is a code over GF(2) with n=600, k=15 and d=272.
This code was found by Heurico 1.16 in 12.5 seconds.